We modify the standard Markov forward noising process that adds noise at each discrete timestep \(t\)  to sample from a wrapped normal instead of a standard normal [1]}:
\(q(x_{t} \mid x_{t-1}) = \mathcal {N}_\text{wrapped} (x_t; \sqrt{1-\beta _t} x_{t-1}, \beta _t I) \propto \sum _{k=-\infty }^{\infty } \exp \left( \frac{- \Vert x_t - \sqrt{1 - \beta _t} x_{t-1} + 2 \pi k \Vert ^2}{2 \beta _t^2} \right)\) 
